The Evolution of Stellar Velocity Dispersion During Dissipationless Galaxy Mergers

Using N-body simulations, we studied the detailed evolution of central stellar velocity dispersion, {\sigma}, during dissipationless binary mergers of galaxies. Stellar velocity dispersion was measured using the common mass-weighting method as well as a flux-weighting method designed to simulate the technique used by observers. A toy model for dust attenuation was introduced in order to study the effect of dust attenuation on measurements of {\sigma}. We found that there are three principal stages in the evolution of {\sigma} in such mergers: oscillation, phase mixing, and dynamical equilibrium. During the oscillation stage, {\sigma} undergoes damped oscillations of increasing frequency. The oscillation stage is followed by a phase mixing stage during which the amplitude of the variations in {\sigma} is smaller and more chaotic than in the oscillation stage. Upon reaching dynamical equilibrium, {\sigma} assumes a stable value. We used our data regarding the evolution of {\sigma} during mergers to characterize the scatter inherent in making measurements of {\sigma} in non-quiescent systems. In particular, we found that {\sigma} does not fall below 70% nor exceed 200% of its final, quiescent value during a merger and that a random measurement of {\sigma} in such a system is much more likely to fall near the equilibrium value than near an extremum. Our toy model of dust attenuation suggested that dust can systematically reduce observational measurements of {\sigma} and increase the scatter in {\sigma} measurements.